Causal reasoning is essential for understanding decision-making about the behaviour of complex `ecosystems' of systems that underpin modern society, with security -- including issues around correctness, safety, resilience, etc. -- typically providing critical examples. We present a theory of strategic reasoning about system modelling based on minimal structural assumptions and employing the methods of transition systems, supported by a modal logic of system states in the tradition of van Benthem, Hennessy, and Milner, and validated through equivalence theorems. Our framework introduces an intervention operator and a separating conjunction to capture actual causal relationships between component systems of the ecosystem, aligning naturally with Halpern and Pearl's counterfactual approach based on Structural Causal Models. We illustrate the applicability through examples of of decision-making about microservices in distributed systems. We discuss localized decision-making through a separating conjunction. This work unifies a formal, minimalistic notion of system behaviour with a Halpern--Pearl-compatible theory of counterfactual reasoning, providing a logical foundation for studying decision making about causality in complex interacting systems.

Model merging via Mixture-of-Experts (MoE) has emerged as a scalable solution for consolidating multiple task-specific models into a unified sparse architecture, where each expert is derived from a model fine-tuned on a distinct task. While effective for multi-task integration, this paradigm introduces a critical yet underexplored challenge: how to attribute and protect the intellectual property (IP) of individual experts after merging. We propose RouteMark, a framework for IP protection in merged MoE models through the design of expert routing fingerprints. Our key insight is that task-specific experts exhibit stable and distinctive routing behaviors under probing inputs. To capture these patterns, we construct expert-level fingerprints using two complementary statistics: the Routing Score Fingerprint (RSF), quantifying the intensity of expert activation, and the Routing Preference Fingerprint (RPF), characterizing the input distribution that preferentially activates each expert. These fingerprints are reproducible, task-discriminative, and lightweight to construct. For attribution and tampering detection, we introduce a similarity-based matching algorithm that compares expert fingerprints between a suspect and a reference (victim) model. Extensive experiments across diverse tasks and CLIP-based MoE architectures show that RouteMark consistently yields high similarity for reused experts and clear separation from unrelated ones. Moreover, it remains robust against both structural tampering (expert replacement, addition, deletion) and parametric tampering (fine-tuning, pruning, permutation), outperforming weight- and activation-based baseliness. Our work lays the foundation for RouteMark as a practical and broadly applicable framework for IP verification in MoE-based model merging.

Learning reduced models from data in a nonintrusive fashion is an important problem in science and engineering [1, 2, 3]. A typical approach is to first learn an encoder-decoder pair, embed the training snapshot trajectories with the learned encoder, and then fit a reduced dynamical-system model to the embedded trajectories. However, the decomposition of the training process into first learning an encoder-decoder pair for the embedding and only sub-sequentially learning a model of the dynamics typically means that the encoder-decoder pair are trained with the objective of accurately approximating the training data, rather than taking the reduced-model prediction error into account. Thus, the encoder-decoder pair can overfit to achieving a low reconstruction error on the training data by learning embeddings of the snapshot trajectories that are non-smooth, which means that learning a reduced model can become challenging. Correspondingly, it has been observed that learning embeddings and models together can be beneficial; see, e.g., [4, 5, 6, 7]. In the context of intrusive model reduction with linear approximations, there is work that optimizes the reduced basis with respect to the model prediction error [8], quantities of interest [9], and to achieve stability [10]; however, we focus here on the setting of nonintrusive model reduction and nonlinear approximations.

In many applications, robots are increasingly deployed in unstructured and natural environments where they encounter various types of vegetation. Vegetation presents unique challenges as a traversable obstacle, where the mechanical properties of the plants can influence whether a robot can safely collide with and overcome the obstacle. A more nuanced approach is required to assess the safety and traversability of these obstacles, as collisions can sometimes be safe and necessary for navigating through dense or unavoidable vegetation. This paper introduces a novel sensor designed to directly measure the applied forces exerted by vegetation on a robot: by directly capturing the push-back forces, our sensor provides a detailed understanding of the interactions between the robot and its surroundings. We demonstrate the sensor's effectiveness through experimental validations, showcasing its ability to measure subtle force variations. This force-based approach provides a quantifiable metric that can inform navigation decisions and serve as a foundation for developing future learning algorithms.

Building energy modeling is a key tool for optimizing the performance of building energy systems. Historically, a wide spectrum of methods has been explored -- ranging from conventional physics-based models to purely data-driven techniques. Recently, hybrid approaches that combine the strengths of both paradigms have gained attention. These include strategies such as learning surrogates for physics-based models, modeling residuals between simulated and observed data, fine-tuning surrogates with real-world measurements, using physics-based outputs as additional inputs for data-driven models, and integrating the physics-based output into the loss function the data-driven model. Despite this progress, two significant research gaps remain. First, most hybrid methods focus on deterministic modeling, often neglecting the inherent uncertainties caused by factors like weather fluctuations and occupant behavior. Second, there has been little systematic comparison within a probabilistic modeling framework. This study addresses these gaps by evaluating five representative hybrid approaches for probabilistic building energy modeling, focusing on quantile predictions of building thermodynamics in a real-world case study. Our results highlight two main findings. First, the performance of hybrid approaches varies across different building room types, but residual learning with a Feedforward Neural Network performs best on average. Notably, the residual approach is the only model that produces physically intuitive predictions when applied to out-of-distribution test data. Second, Quantile Conformal Prediction is an effective procedure for calibrating quantile predictions in case of indoor temperature modeling.

This letter develops a novel physics-informed neural ordinary differential equations-based framework to emulate the proprietary dynamics of the inverters -- essential for improved accuracy in grid dynamic simulations. In current industry practice, the original equipment manufacturers (OEMs) often do not disclose the exact internal controls and parameters of the inverters, posing significant challenges in performing accurate dynamic simulations and other relevant studies, such as gain tunings for stability analysis and controls. To address this, we propose a Physics-Informed Latent Neural ODE Model (PI-LNM) that integrates system physics with neural learning layers to capture the unmodeled behaviors of proprietary units. The proposed method is validated using a grid-forming inverter (GFM) case study, demonstrating improved dynamic simulation accuracy over approaches that rely solely on data-driven learning without physics-based guidance.

Accurately modeling malware propagation is essential for designing effective cybersecurity defenses, particularly against adaptive threats that evolve in real time. While traditional epidemiological models and recent neural approaches offer useful foundations, they often fail to fully capture the nonlinear feedback mechanisms present in real-world networks. In this work, we apply scientific machine learning to malware modeling by evaluating three approaches: classical Ordinary Differential Equations (ODEs), Universal Differential Equations (UDEs), and Neural ODEs. Using data from the Code Red worm outbreak, we show that the UDE approach substantially reduces prediction error compared to both traditional and neural baselines by 44%, while preserving interpretability. We introduce a symbolic recovery method that transforms the learned neural feedback into explicit mathematical expressions, revealing suppression mechanisms such as network saturation, security response, and malware variant evolution. Our results demonstrate that hybrid physics-informed models can outperform both purely analytical and purely neural approaches, offering improved predictive accuracy and deeper insight into the dynamics of malware spread. These findings support the development of early warning systems, efficient outbreak response strategies, and targeted cyber defense interventions.

Weak form Scientific Machine Learning (WSciML) is a recently developed framework for data-driven modeling and scientific discovery. It leverages the weak form of equation error residuals to provide enhanced noise robustness in system identification via convolving model equations with test functions, reformulating the problem to avoid direct differentiation of data. The performance, however, relies on wisely choosing a set of compactly supported test functions. In this work, we mathematically motivate a novel data-driven method for constructing Single-scale-Local reference functions for creating the set of test functions. Our approach numerically approximates the integration error introduced by the quadrature and identifies the support size for which the error is minimal, without requiring access to the model parameter values. Through numerical experiments across various models, noise levels, and temporal resolutions, we demonstrate that the selected supports consistently align with regions of minimal parameter estimation error. We also compare the proposed method against the strategy for constructing Multi-scale-Global (and orthogonal) test functions introduced in our prior work, demonstrating the improved computational efficiency.

Physics phenomena are often described by ordinary and/or partial differential equations (ODEs/PDEs), and solved analytically or numerically. Unfortunately, many real-world systems are described only approximately with missing or unknown terms in the equations. This makes the distribution of the physics model differ from the true data-generating process (DGP). Using limited and unpaired data between DGP observations and the imperfect model simulations, we investigate this particular setting by completing the known-physics model, combining theory-driven models and data-driven to describe the shifted distribution involved in the DGP. We present a novel hybrid generative model approach combining deep grey-box modelling with Optimal Transport (OT) methods to enhance incomplete physics models. Our method implements OT maps in data space while maintaining minimal source distribution distortion, demonstrating superior performance in resolving the unpaired problem and ensuring correct usage of physics parameters. Unlike black-box alternatives, our approach leverages physics-based inductive biases to accurately learn system dynamics while preserving interpretability through its domain knowledge foundation. Experimental results validate our method's effectiveness in both generation tasks and model transparency, offering detailed insights into learned physics dynamics.

Causal reasoning capability is critical in advancing large language models (LLMs) toward strong artificial intelligence. While versatile LLMs appear to have demonstrated capabilities in understanding contextual causality and providing responses that obey the laws of causality, it remains unclear whether they perform genuine causal reasoning akin to humans. However, current evidence indicates the contrary. Specifically, LLMs are only capable of performing shallow (level-1) causal reasoning, primarily attributed to the causal knowledge embedded in their parameters, but they lack the capacity for genuine human-like (level-2) causal reasoning. To support this hypothesis, methodologically, we delve into the autoregression mechanism of transformer-based LLMs, revealing that it is not inherently causal. Empirically, we introduce a new causal Q&A benchmark called CausalProbe-2024, whose corpora are fresh and nearly unseen for the studied LLMs. The LLMs exhibit a significant performance drop on CausalProbe-2024 compared to earlier benchmarks, indicating the fact that they primarily engage in level-1 causal reasoning. To bridge the gap towards level-2 causal reasoning, we draw inspiration from the fact that human reasoning is usually facilitated by general knowledge and intended goals. We propose G^2-Reasoner, a method that incorporates general knowledge and goal-oriented prompts into LLMs' causal reasoning processes. Experiments demonstrate that G^2-Reasoner significantly enhances LLMs' causal reasoning capability, particularly in fresh and counterfactual contexts. This work sheds light on a new path for LLMs to advance towards genuine causal reasoning, going beyond level-1 and making strides towards level-2.